Specimen 1 2 3 4 5 6 7 8 9
Steel ball 50 57 61 70 68 54 65 51 53
Diamond 52 55 63 74 69 55 68 51 56
The manufacturer of hardness testing equipment uses steel-ball indenters to penetrate metal that is being tested. However, the manufacturer thinks it would be better to use a diamond indenter so that all types of metal can be tested. Because of differences between the two types of indenters, it is suspected that the two methods will produce different hardness readings. The metal specimens to be tested are large enough so that two indentions can be made.Therefore, the manufacturer uses both indenters on each specimen and compares the hardness readings. Construct a 95% confidence interval to judge whether the two indenters result in different measurements.
Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers.
Construct a 95% confidence interval to judge whether the two indenters result in different measurements, where the differences are computed as 'diamond minus steel ball'.
n1 = n2 = n = 9, d-bar = 1.5556, s = 1.8105, Confidence level = 95%
Degrees of freedom = n - 1 = 8
SE = s/√n = 0.6035
t- score = 2.306004133
Margin of error = t * SE = 1.3917
The 95% confidence interval is [1.5556 - 1.3917, 1.5556 + 1.3917] = [0.164, 2.947]
The above confidence interval does not contain 0. This means there is enough evidence that the two indenters result in significantly different measurements.
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